一类食饵具有常数收获率和Holling Ⅲ型功能性反应的捕食者-食饵模型的定性分析

A Qualitative Analysis of Holling Ⅲ Predator-Prey System with Constant Harvesting Rate

本文对捕食者种群、食饵种群均在线性密度制约的条件下,食饵种群具有常数收获率的HollingⅢ型功能性反应模型进行定性分析,通过运用定性分析的方法和利用Dulac函数方法,分别讨论了模型正平衡点稳定性、极限环的存在性以及无穷远奇点的稳定性,得到了正平衡点存在的条件和在其周围不存在极限环的条件,以及无穷远点的性态,并给出了模型轨线的全局结构图.最后,对该模型作了数值的仿真模拟验证.

In this thesis we study the model of Predator-Prey of Holling's III with linear density restriction on both predator and prey.The stability of the unique positive equilibrium and the existence of limit cycle are investigated,including the stability of infinity.By using qualitative theory of ordinary differential equation,we obtain the sufficient conditions of the unique positive equilibrium and the criteria of the nonexistence of limit cycle.The global phase portraits as well as numerical simulation are given.